How to Add Background Images in 2.8 and later
You can do this in Blender 2.81 by pressing Shift+A then going to Image > Reference. In all honesty, it doesn't matter whether you choose reference or background. The added image will be directly facing the viewport camera at the time of adding it, so align your viewport to the correct orientation you want the image to first.

When you select the image, you will have an Object Data Properties tab with a picture icon on the right side menu. Click on it and you can now change the settings for the image.


If you check Use Alpha and change the Transparency bar, you can change the transparency of the object. Changing Depth will cause the image to be displayed in front of or behind your objects. Changing Side will allow you to see it only from the front/back, useful if you have both front and back reference photos.

The Display Orthographic and Display Perspective checkboxes allow you to decide if you want to be able to see the reference in the respective view modes.

You might find that being able to select your reference image while editing is annoying. In the top right corner, click on the Filter button, and under Restriction Toggles, enable the Selectable option (its an icon of a cursor). Now, just disable the Selectable icon next to the reference image and you can no longer select it.